Problem: Solve for $x$. $9^6=x^3\cdot9^3$ $x=$
When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${9^6}={x^3}\cdot9^3}$. $\begin{aligned} &={\underbrace{x\cdot x\cdot x}_\text{3 times}}\cdot\underbrace{9\cdot9\cdot9}_\text{3 times}} \\\\\\ &={\underbrace{9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9}_\text{6 times}} \\\\ \end{aligned}$ $x=9$